Abstract
Three-way decision (3WD) is a decision that conforms to human's cognitive pattern and offers a new visual angle for solving practical decision-making problems. An information system (IS) represents relationships between objects and attributes. And a multi-source information system (MSIS) is an IS which composes of multi-source data sets. This paper presents 3WD in an MSIS as well as gives its application in petroleum project investment. Considering that risks are uncertain, loss functions are first given by means of interval numbers. Then, multi-granulation decision-theoretic rough set (MGDTRS) models in a given MSIS are proposed from the point of view of multi-granulation. Next, based on the idea of a decision-theoretic rough set (DTRS), the optimistic and pessimistic 3WDs in the MSIS are proposed. Finally, an example of petroleum project investment is used to support the feasibility of the proposed decision method.
Highlights
The idea of three-way decision (3WD), introduced by Yao [42]–[45] that generated from the extended of decision rough sets and the related conclusions of many disciplines
decision-theoretic rough set (DTRS) model systematically calculates thresholds from loss functions by using the distinguished bayesian decision theory. This model utilizes equivalence relation to divide the universe into many equivalence classes, introduces upper and lower approximations to characterize the uncertainty of system
3WD is proposed on the basis of DTRS model and decision rules contain three kinds: the rule that is generated from the positive region represents accepting something; the rule that is
Summary
The idea of three-way decision (3WD), introduced by Yao [42]–[45] that generated from the extended of decision rough sets and the related conclusions of many disciplines. DTRS model systematically calculates thresholds from loss functions by using the distinguished bayesian decision theory This model utilizes equivalence relation to divide the universe into many equivalence classes, introduces upper and lower approximations to characterize the uncertainty of system. Yao and Zhou [50] proposed a DTRS model with naive Bayesian decision theory, which provides a practicable way for assessing conditional probability in 3WD; Yao et al [46], [51] analyzed the related attributes of 3WD and proved the superiority of 3WD; Greco et al [7] took into account the cost of misclassification, and presented three-way probability models under the advantage relation; Mandal et al [31] discussed three-way decisions with multigranulation interval-valued fuzzy probabilistic rough sets.
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